The time constants of integrated systems have been traditionally implemented using transconductors and capacitors (T=C/gm). Cut off programmability is achieved by controlling the transconductance gain gm. FIG. 1 shows a typical CMOS differential transconductor for which the following equations apply: EQU ID=1/2*u*Cox*W/L*Vod 2 (1)
where:
Vod=VGS-VTH EQU gm=dID/dVGS=u*Cox*W/L*Vod (2) PA1 ID is the drain current PA1 u is the nobility PA1 Cox is the specific capacitance of PA1 the oxide PA1 W is the channel width PA1 L is the channel length PA1 Vod is the so-called "overdrive" voltage of a MOS transistor
where:
For a given transistor's dimensioning (W/L), the maximum value of the transconductance gain gm is limited by the fact that the overdrive voltage Vod of the differential stage cannot exceed a certain value. Otherwise, the bias current generator of the stage could be turned off. In contrast, the minimum value of the current gain gm is limited by the fact that if the overdrive voltage Vod decreases the same amplitude of the input signal, the distortion that is introduced on the output current delivered by the transconductor stage increases.
The current output by the transconductor is directly proportional to the input voltage Vin only if such current is relatively small if compared to the overdrive voltage Vod. The distortion caused by the transconductor at relatively low values of the overdrive voltage Vod may be reduced by introducing, for this purpose, a number of degeneration resistors, as shown in FIG. 2.
By defining gm1 as the transconductance of the single input MOS transistor, the stage transconductance may be expressed as: EQU gm=gm1/(1+R*gm1) (3)
In the known structure of FIG. 2, part of the input signal drops due to the degeneration resistance. Therefore, for the same amplitude of the input signal, the voltage vgs between the gate and the source has a reduced range and a reduced distortion, according to the expression: ##EQU1##
For the same absorbed power and overdrive, a greater linearity is obtained at the expense of a lower transconductance gain.
A disadvantage of this known structure is that the transconductance attenuation caused by the source degeneration resistance, introduced to improve the linearity at low overdrive levels, increases as the overdrive voltage increases. The result is a reduction of the trimming range of the circuit.